Scotland is a big place and there is allot to see in every location. Additionally, the roads on the west coast, such as in Skye, are not fast roads. They twist and turn around mountains and lochs. 20 miles as the crow flies could work out as 100 miles of actual driving. To cover all those locations you'd spend about 4 days constantly driving and you'd really see nothing. Focus on say 3 days for one or two cities and then the rest of the week for highland touring.
The order of events might be different from what I post. Scottish weather is very changeable. You should try to do city based things on wet days and keep drives in the countryside to sunny days.
For cheap accommodation, opt for Bed and Breakfast (B&B) rather than hotels. Youth hostels are also a good option. Remember that in peak season, accommodation can be scarce. Book in advance and make use of the Tourist Information centres in each town/village to find out about availability.
Day 1: Edinburgh:
Start at the castle: budget about 2 hours to see around.
Camera Obscura: Next to the castle entrance and has interesting displays and views of the whole city. Budget an hour.
Walk down the Royal Mile. On the way, stop into St. Gyles Cathedral (20 mins). Find a restaurant near here to eat lunch.
Continue down the Mile and visit Hollyrood Palace and the nearby Parliament buildings.
If the weather is fine, go to one of the parks for late afternoon. Such as Hollyrood, Princes Gardens, Botanical Gardens. If the weather is poor, head to one of the many museums or the National Gallery.
Day 2: Glasgow:
Do this on a wet day as it's mostly indoors stuff.
Museums: Choose one of: Transport Museum, Kelvengrove Museum and Art Gallery, Clyde Built, Science Museum, Scotland Street School Museum.
Glasgow has some of the best Indian restaurants. Best time to go is lunch time as most do a low priced lunch menu. Afternoon go shopping in the city centre. Pop into Willow Tea Rooms for afternoon tea, coffee and scones and enjoy the Art Deco furnishings created by Rennie Mackintosh. Late afternoon go to the Necropolis for a atmospheric, if spooky, end to the day. In the evening, enjoy the Glasgow night life in the Merchant City and around George Square.
In my opinion, the highlands are best approached from Glasgow rather than from Edinburgh. The A81/A812 runs north through the Trossachs. The A82 runs up Loch Lomond side, through Glen Coe and on up to Fort William, Loch Ness and Inverness. The A83 will take you norht then west into Argyle
Day 3: Loch Lomond and the Trossachs National Park:
Head out of Glasgow on the A81 towards Aberfoyle. Stop in at the Glengoyne Distillery to sample the whisky. Remember no drinking and driving. When you get near Aberfoyle, turn left onto the A821. Pause occasional to admire the views. Stop at Loch Katrine and take the steam boat up and down the loch. Continue on the A821 then right onto the A85 to Callader. Walk through the village and find somewhere here for lunch. Backtrack on the A85 and head north. Again Pausing occasionally at view points. Continue north and west to Crianlarich then turn south on the A82. At Tarbot, turn left onto the A83 and continue towards Inveraray. Find lodings near here for the night.
Day 4: Argyle:
After viewing Ineraray Jail and the Castle, drive south on the A83 to Lochgilphead. Turn left onto the A816 and head north. Stop of at the ancient ruins along this road including Dunadd fort site, the stone circles and chamber cairns at and the church and ancient gravestones at Kilmartin Church and the neighbouring house museum. There is also the ruined Carnasserie Castle in this area which is worth looking at. Continue on to Oban. Lodge here overnight. Visit the McCaigs Tower and walk along the sea front. This is an excellent place to try the Scottish favourite dish - Fish & Chips. For the best experience, take the food out of the restaurant and eat on the sea front.
Day 5: Islands:
No trip to Scotland would be complete without visiting on of the islands. Leaving the car in Oban, take the ferry to Mull. Ferries run from Oban to the Isle of Mull and back 6 times daily in summer. Timetables are online at http://www.calmac.co.uk. On the island you have a choice of things to see, but not time for everything. Either head south to Iona Abby. This famous Christian site is very interesting. Or else go north to Tobermory - picturesque fishing village. Since you are not driving, you may stop in a the Tobermory Distillery and enjoy a dram of whisky. There is also a distillery in Oban too. Make sure you get back in time for the last ferry to Oban. Again overnight here.
Day 6: Glen Coe:
Take the A85 east out of Oban, pause to view the Falls of Laura at Connel Bridge then head north on the A828 towards Fort William. Pause just outside Portnacoish to view the scenery overlooking Castle Stalker. Try to find some hotel before Ballachulish for lunch. Join the A82 east/south signed for Glasgow. This will take you through Glen Coe. Drive into Glen Coe village follow signs for the Hospital and then Glen Coe Lochann. The small Loch makes for a pleasant walk in the highland scenery. Return to the A82 and drive through Glen Coe to Rannoch moor, through Bridge of Orchay and on south to Glasgow. Remember to pause wherever you find a good view with favourable weather along the way. On return to Glasgow, deposit you rental car.
Day 7: Back in Glasgow:
Depending on how much time you have left, there are other trips to consider around Glasgow. Day trips to the Isle of Arran or Isle of Bute by train and ferry are easily done.